Related papers: Limits of some weighted Cesaro averages
Fluctuations of the order parameters of the Gardner model for any $\alpha<\alpha_c$ are studied. It is proved that they converge in distribution to a family of jointly Gaussian random variables.
We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…
In this paper, we establish some theorems on the distribution of primes in higher-order progressions on average.
We provide the analytic forms of the distributions for the sum of ordered spacings. We do this both for the case where the boundaries are included in the calculation of the spacings and the case where they are excluded. Both the probability…
We develop a theory of limits of finite posets in close analogy to the recent theory of graph limits. In particular, we study representations of the limits by functions of two variables on a probability space, and connections to…
A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out…
The convergence of partial sums and Ces\'aro means of negative order of double Walsh-Fourier series of functions of bounded \ generalized variation is investigated.
We obtain a Burgess-type bound for character sums over unions of intervals. The result follows from the argument of Heath-Brown, with an improvement in one of the steps.
We give some bounds on edge Folkman numbers.
In this article, we investigate high moments of zeta sums $\sum_{n\le x}n^{i t}$. We show unconditional lower bounds for them.
Under Poincar\'e-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on improved concentration inequalities on high-dimensional…
Under correlation-type conditions, we derive upper bounds of order $\frac{1}{\sqrt{n}}$ for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law.
We study pattern densities in binary sequences, finding optimal limit sequences with fixed pattern densities.
We consider weighted averages of the number of representations of an even integer as a sum of two prime numbers, where each summand lies in a given arithmetic progression modulo a common integer $q$. Our result is uniform in a suitable…
We study a generalized Abreu equation and derive some estimates.
Under correlation-type conditions, we derive an upper bound of order $(\log n)/n$ for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved…
We present factorizations of weighted Lebesgue, Ce\-s\` aro and Copson spaces, for weights satisfying the conditions which assure the boundedness of the Hardy's integral operator between weighted Lebesgue spaces. Our results enhance, among…
We study the higher order q- Poincar\'e and other coercive inequalities for a class probability measures satisfying Adam's regularity condition.
We give a proof of some small weight and level cases of Serre's conjecture.
We extend Carleson's formula to radially polynomially weighted Dirichlet spaces.